Geodesic
Dirichlet Problem for a Class of Quasilinear Elliptic Equations
Matematičeskie zametki, Tome 76 (2004) no. 4, pp. 592-603

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In this paper, the Dirichlet problem for quasilinear elliptic equations is studied. New a priori estimates of the solution and its gradient are obtained. These estimates are derived without any assumptions on the smoothness of the coefficients and the right-hand side of the equation. Moreover, an arbitrary growth of the right-hand side with respect to the gradient of the solution is assumed. On the basis of the resulting estimates, existence theorems are proved. 
@article{MZM_2004_76_4_a10,
     author = {A. S. Tersenov},
     title = {Dirichlet {Problem} for a {Class} of {Quasilinear} {Elliptic} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {592--603},
     publisher = {mathdoc},
     volume = {76},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_4_a10/}
}
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A. S. Tersenov. Dirichlet Problem for a Class of Quasilinear Elliptic Equations. Matematičeskie zametki, Tome 76 (2004) no. 4, pp. 592-603. http://geodesic.mathdoc.fr/item/MZM_2004_76_4_a10/